This invention pertains to the layup of the fully isotropic laminates and quasi-homogeneous anisotropic laminates.
A laminate is a flat plate or curved shell consisting of two or more plies stacked and bonded as an integral component for structural applications. Each ply is a uniform-thickness layer of an orthotropic or anisotropic material. FIG. 1 shows an exploded view of a typical flat laminate. The arrangement of the material, thickness, orientation, and stacking sequence of the plies is referred to as the "layup" of the laminate. The layup of a laminate is generally tailored to match the stiffness and strength requirements for loadings in various directions.
FIGS. 2(a) and 2(b) illustrate the definitions of the coordinate system and the mechanical loadings (extension, shear, bending, and twisting) on a flat laminate.
Fiber-reinforced composite laminates such as graphite/epoxy and Kevlar/epoxy are ideal for structural applications where high strength-to-weight and stiffness-to-weight ratios are desired for weight reduction (e.g. aircraft and spacecraft structures). In addition, composite laminates are superior in corrosion resistance, acoustic damping, fatigue life, thermal insulation, and many other applications.
FIGS. 3(a) and 3(b) show polar plots of the extensional and bending stiffnesses of an example graphite/epoxy laminate, respectively. The length of d indicates the magnitude of the laminate stiffness with respect to the loading in direction .theta.. Since the laminate stiffnesses vary with .theta., the laminate is said to be anisotropic. Note that the degree of anisotropy in the extension and bending stiffnesses are different, which is typical of composite laminates.
The concept of in-plane isotropic laminates was discovered by F. Weiren and C. B. Norris as described in "Mechanical Properties of a Laminate Designed to be Isotropic," Report No. 1841, Forest Products Laboratory, Forest Service, U.S. Department of Agriculture, May 1953. FIGS. 4(a) and 4(b) show plots of the extensional and the bending stiffness of such laminates, respectively. In-plane isotropy is characterized by a circular pattern of extensional stiffness; while out-of-plane bending stiffness remains anisotropic. Hence, for the past few decades, a laminates with in-plane isotropy and a symmetric layup has been referred to as an "extensionally isotropic laminate" (hereinafter designated as EIL).
As of today, the tailoring technology for composite laminate is in a state of continuing improvement for meeting various engineering requirements.
The present invention discovers the layups of
i. the fully isotropic laminate (hereinafter designated as FIL) that exhibits the stiffness isotropy --as in a homogeneous isotropic plate--concomitant in extension, shear, bending, and twisting; and
ii. the quasi-homogeneous anisotropic laminate (hereinafter designated as QHAL) that has identical stiffness anisotropy--as in a homogeneous anisotropic plate--in extension and bending as well as in shear and twisting.
The FIL layup developed in the present invention combines an EIL layup with out-of-plane isotropy (bending and twisting). As illustrated in FIGS. 5(a) and 5(b), both extensional and bending stiffnesses of an FIL are indicated by circles for isotropy. The isotropy also exists in the shear and twisting stiffnesses of an FIL layup; we thus refer to the layup as the fully isotropic laminate.
The QHAL layup developed in the present invention provides identical anisotropy in a laminate for both in-plane and out-of-plane stiffnesses. The term "identical anisotropy" stipulates that the stiffness directionalities are identical with respect to extension and bending, as well as to shear and twisting. FIGS. 6(a) and 6(b) show polar plots of the extensional and bending stiffnesses of a QHAL, respectively. Although both stiffnesses are anisotropic, the anisotropy is identical with respect to the angle .theta.. This characteristic has been found only in homogeneous anisotropic plates; but has never been achieved with a multiply multiangle laminate. We thus refer to the layup as the quasi-homogeneous anisotropic laminate.
The FIL and the QHAL have distinctive applications for load-carrying laminates,
i. An FIL provides the same stiffness reinforcement in all directions, which eliminates the concern for the "weak aspect" in the structural element and eases the engineering consideration of composite laminates.
ii. A QHAL, with identical anisotropy for both in-plane and out-of-plane stiffnesses, provides the maximum (and minimum) in-plane and out-of-plane reinforcements in the same direction. Thus, a QHAL is a layup for maximum weight reduction in a laminated structure.
The approaches and models for generating these layups are closely related; they are described in layer sections.
In a 1979 General Motors research report (EM-429, GM restricted), "Isotropic Composite Plates--A Conceptual Approach," K. M. Wu, one of the inventors of the present invention, described the approach for developing the FIL. However, due to an incomplete solution scheme, no FIL was discovered.
U.S. Pat. No. 4,882,230 (1989) to S. B. Warner relates to a process for producing a multilayer polymeric film having dead bend characteristics which are substantially planar (in-plane) isotropic. According to the patent, the highly oriented polymeric films are laminated to form a good food wrap that can remain in the deformed state. Except for including the publicized concept of in-plane isotropy and the method of masking dead bend polymeric film, this process involves no technology that could lead to any part of the present invention.